Finite Group Databasebeta

← C59×#33560 #28445669

Subgroups — C59×#33560 #28445669

Order 15104.

1132 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3551C211yesmaximal, characteristic, complemented
2C59×#3028C211yesmaximal, characteristic, complemented
3C59×#3027C211yesmaximal, characteristic, complemented
4C59×#3018C211yesmaximal, characteristic, complemented
5C59×#2200C214yesmaximal, complemented
6C59×#2197C214yesmaximal, complemented
7C59×#2126C211yesmaximal, characteristic, complemented
8C59×#2123C211yesmaximal, characteristic, complemented
9C59×#2122C211yesmaximal, characteristic, complemented
10C59×#585C2211yescharacteristic
11C59×#575—21no—
12C59×#563—21no—
13C59×#560C2212yescomplemented
14C59×#555—21no—
15C59×#553—21no—
16C59×#552—21no—
17C59×#551C2212yescomplemented
18C59×#548—21no—
19C59×#546—21no—
20C59×#540—22no—
21C59×#538—22no—
22C59×#537—21no—
23C59×#536—21no—
24C59×#536C2211yescharacteristic
25C59×#535—21no—
26C59×#535C2211yescharacteristic
27C59×#532C2211yescharacteristic
28C59×#529—21no—
29C59×#458—22no—
30C59×#458C2214yes—
31C59×B(4,𝔽2)—22no—
32C59×B(4,𝔽2)C2214yes—
33C59×#456—21no—
34C59×#455C2212yes—
35C59×#454—21no—
36C59×#453C2212yes—
37C2×#104×C59—21no—
38C59×#413C2211yescharacteristic
39C59×#410—21no—
40C59×#410—21no—
41C59×#410C2211yescharacteristic
42C59×#410C2211yescharacteristic
43C59×#354C2212yescomplemented
44C59×#353C2212yescomplemented
45C59×#352C2214yescomplemented
46C59×AΣL(1,𝔽16)C2214yescomplemented
472−1+4×C59—21no—
482−1+4×C59—41no—
49H(5,𝔽2)×C59—21no—
50H(5,𝔽2)×C59—21no—
51H(5,𝔽2)×C59—41no—
52H(5,𝔽2)×C59C2312yes—
53C2×#41×C59—21no—
54C2×#41×C59—21no—
55C2×#41×C59—21no—
56C2×#41×C59—21no—
57C2×#41×C59—42no—
58C2×#41×C59D411yescharacteristic, complemented
59C2×#41×C59C2311yescharacteristic
60C22×Q8×C59D411yescharacteristic, complemented
61C22×D4×C59D411yescharacteristic
62#137×C59—22no—
63#137×C59—41no—
64AGL(1,ℤ/8)×C59—22no—
65AGL(1,ℤ/8)×C59—41no—
66#135×C59—42no—
67C2×M16×C59—21no—
68C4⋊Q8×C59—21no—
69C4⋊Q8×C59—41no—
70C4⋊Q8×C59D411yescharacteristic, complemented
71#127×C59—21no—
72#127×C59—41no—
73#127×C59C2311yescharacteristic
74#126×C59—22no—
75#126×C59—22no—
76#126×C59—22no—
77#125×C59—21no—
78#125×C59—22no—
79#124×C59—21no—
80#124×C59—22no—
81#124×C59—21no—
82#124×C59—21no—
83#124×C59—41no—
84#124×C59—41no—
85#124×C59D411yescharacteristic, complemented
86#124×C59C2311yescharacteristic
87#123×C59—22no—
88#123×C59—22no—
89#123×C59—22no—
90#123×C59—22no—
91#123×C59—24no—
92#123×C59D412yescomplemented
93#123×C59C2312yes—
94C22⋊Q8×C59—21no—
95C22⋊Q8×C59—22no—
96C22⋊Q8×C59—22no—
97C22⋊Q8×C59—21no—
98C22⋊Q8×C59—21no—
99C22⋊Q8×C59—42no—
100#121×C59—22no—
101#121×C59—22no—
102#121×C59—21no—
103#121×C59—22no—
104#121×C59—21no—
105#121×C59—21no—
106#121×C59—22no—
107#121×C59—21no—
108#121×C59—21no—
109#121×C59—22no—
110#121×C59—22no—
111#121×C59—42no—
112#120×C59—22no—
113#120×C59—24no—
114#120×C59D412yes—
115#120×C59C2312yes—
116C4×Q8×C59—21no—
117C4×D4×C59—22no—
118C4×D4×C59—21no—
119C4×D4×C59—22no—
120C4×D4×C59—21no—
121C4×D4×C59—21no—
122C4×D4×C59—22no—
123#117×C59—22no—
124#117×C59—22no—
125#117×C59—21no—
126#117×C59—21no—
127#117×C59D411yescharacteristic
128#117×C59D411yescharacteristic, complemented
129C2×C4⋊C4×C59—21no—
130C2×C22⋊C4×C59—22no—
131C2×C42×C59D411yescharacteristic, complemented
132#104×C59—22no—
133#104×C59—22no—
134#101×C59—21no—
135#100×C59C2312yes—
136#99×C59—21no—
137#99×C59—21no—
138#99×C59—24no—
139#99×C59—24no—
140#99×C59C2312yes—
141#99×C59C2312yes—
142C24×C59C2×D412yes—
143#41×C59—22no—
144#41×C59—22no—
145#41×C59—41no—
146#41×C59—41no—
147#41×C59—42no—
148#41×C59—41no—
149#41×C59—41no—
150#41×C59—41no—
151#41×C59—41no—
152#41×C59—41no—
153#41×C59—42no—
154#41×C59—42no—
155#41×C59—41no—
156#41×C59—41no—
157#41×C59—42no—
158#41×C59—41no—
159#41×C59—41no—
160#41×C59—41no—
161#41×C59—81no—
162#41×C59—81no—
163C2×Q8×C59—21no—
164C2×Q8×C59—21no—
165C2×Q8×C59—21no—
166C2×Q8×C59—21no—
167C2×Q8×C59—21no—
168C2×Q8×C59—41no—
169C2×Q8×C59—41no—
170C2×Q8×C59—42no—
171C2×Q8×C59C2×D411yescharacteristic
172C2×Q8×C59C2×D411yescharacteristic
173C2×D4×C59—21no—
174C2×D4×C59—21no—
175C2×D4×C59—21no—
176C2×D4×C59—22no—
177C2×D4×C59—22no—
178C2×D4×C59—22no—
179C2×D4×C59—22no—
180C2×D4×C59—22no—
181C2×D4×C59—21no—
182C2×D4×C59—21no—
183C2×D4×C59—22no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—41no—
188C2×D4×C59—41no—
189C2×D4×C59—42no—
190C2×D4×C59—42no—
191C2×D4×C59—42no—
192C2×D4×C59—41no—
193C2×D4×C59—44no—
194C2×D4×C59C2×D411yescharacteristic
195C2×D4×C59C2×D411yescharacteristic
196C2×D4×C59C2×D411yescharacteristic
197C2×D4×C59C2411yescharacteristic
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59—22no—
201C22×C4×C59—22no—
202C22×C4×C59—22no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—41no—
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D412yes—
210Q16×C59—42no—
211SD16×C59—42no—
212SD16×C59—42no—
213D8×C59—42no—
214M16×C59—22no—
215M16×C59—41no—
216C2×C8×C59—41no—
217C4⋊C4×C59—22no—
218C4⋊C4×C59—22no—
219C4⋊C4×C59—22no—
220C4⋊C4×C59—22no—
221C4⋊C4×C59—22no—
222C4⋊C4×C59—22no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—21no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59—22no—
228C4⋊C4×C59—41no—
229C4⋊C4×C59—41no—
230C4⋊C4×C59—44no—
231C22⋊C4×C59—22no—
232C22⋊C4×C59—22no—
233C22⋊C4×C59—22no—
234C22⋊C4×C59—22no—
235C22⋊C4×C59—22no—
236C22⋊C4×C59—22no—
237C22⋊C4×C59—21no—
238C22⋊C4×C59—22no—
239C22⋊C4×C59—21no—
240C22⋊C4×C59—21no—
241C22⋊C4×C59—21no—
242C22⋊C4×C59—22no—
243C22⋊C4×C59—22no—
244C22⋊C4×C59—22no—
245C22⋊C4×C59—22no—
246C22⋊C4×C59—44no—
247C22⋊C4×C59—44no—
248C22⋊C4×C59C2×D412yes—
249C22⋊C4×C59C2×D412yes—
250C42×C59—22no—
251C42×C59—21no—
252C42×C59—21no—
253C42×C59—21no—
254C42×C59—41no—
255C42×C59—41no—
256C42×C59C2×D411yescharacteristic
257C42×C59C2×D411yescharacteristic
258C23×C59—22no—
259C23×C59—22no—
260C23×C59—22no—
261C23×C59—21no—
262C23×C59—41no—
263C23×C59—42no—
264C23×C59—82no—
265C23×C59#12011yescharacteristic
266C23×C59C22×D411yescharacteristic
267C23×C59C22×D411yescharacteristic
268Q8×C59—22no—
269Q8×C59—41no—
270Q8×C59—41no—
271Q8×C59—41no—
272Q8×C59—41no—
273Q8×C59—41no—
274Q8×C59—41no—
275Q8×C59—41no—
276Q8×C59—81no—
277D4×C59—22no—
278D4×C59—41no—
279D4×C59—41no—
280D4×C59—41no—
281D4×C59—41no—
282D4×C59—41no—
283D4×C59—41no—
284D4×C59—42no—
285D4×C59—42no—
286D4×C59—42no—
287D4×C59—42no—
288D4×C59—41no—
289D4×C59—41no—
290D4×C59—41no—
291D4×C59—81no—
292D4×C59—81no—
293D4×C59—82no—
294D4×C59—82no—
295D4×C59—82no—
296D4×C59—81no—
297D4×C59—81no—
298D4×C59—82no—
299D4×C59—164no—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—21no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—21no—
309C2×C4×C59—22no—
310C2×C4×C59—21no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—21no—
314C2×C4×C59—42no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—41no—
318C2×C4×C59—42no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—42no—
322C2×C4×C59—42no—
323C2×C4×C59—42no—
324C2×C4×C59—82no—
325C2×C4×C59—81no—
326C2×C4×C59—82no—
327C2×C4×C59—82no—
328C2×C4×C59#12011yescharacteristic
329C2×C4×C59#12011yescharacteristic
330C2×C4×C59#12011yescharacteristic
331C2×C4×C59C22×D411yescharacteristic
332C8×C59—42no—
333#33560C5911yesmaximal, characteristic, direct product factor, Sylow
334C22×C59—21no—
335C22×C59—21no—
336C22×C59—21no—
337C22×C59—41no—
338C22×C59—41no—
339C22×C59—41no—
340C22×C59—41no—
341C22×C59—42no—
342C22×C59—41no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—41no—
346C22×C59—42no—
347C22×C59—82no—
348C22×C59—84no—
349C22×C59—82no—
350C22×C59—161no—
351C22×C59C2×#12011yescharacteristic
352C4×C59—21no—
353C4×C59—21no—
354C4×C59—21no—
355C4×C59—41no—
356C4×C59—42no—
357C4×C59—42no—
358C4×C59—41no—
359C4×C59—42no—
360C4×C59—41no—
361C4×C59—42no—
362C4×C59—82no—
363C4×C59—82no—
364C4×C59B(4,𝔽2)11yescharacteristic
365C4×C59B(4,𝔽2)11yescharacteristic
366#3551C2×C5911yescharacteristic, complemented
367#3028C2×C5911yescharacteristic, complemented
368#3027C2×C5911yescharacteristic, complemented
369#3018C2×C5911yescharacteristic, complemented
370#2200C2×C5914yescomplemented
371#2197C2×C5914yescomplemented
372#2126C2×C5911yescharacteristic, complemented
373#2123C2×C5911yescharacteristic, complemented
374#2122C2×C5911yescharacteristic, complemented
375C2×C59—21no—
376C2×C59—41no—
377C2×C59—41no—
378C2×C59—41no—
379C2×C59—81no—
380C2×C59—82no—
381C2×C59—82no—
382C2×C59C2×B(4,𝔽2)11yescharacteristic
383#585C22×C5911yescharacteristic
384#575—21no—
385#563—21no—
386#560C22×C5912yescomplemented
387#555—21no—
388#553—21no—
389#552—21no—
390#551C22×C5912yescomplemented
391#548—21no—
392#546—21no—
393#540—22no—
394#538—22no—
395#537—21no—
396#536—21no—
397#536C22×C5911yescharacteristic
398#535—21no—
399#535C22×C5911yescharacteristic
400#532C22×C5911yescharacteristic
401#529—21no—
402#458—22no—
403#458C22×C5914yes—
404B(4,𝔽2)—22no—
405B(4,𝔽2)C22×C5914yes—
406#456—21no—
407#455C22×C5912yes—
408#454—21no—
409#453C22×C5912yes—
410C2×#104—21no—
411#413C22×C5911yescharacteristic
412#410—21no—
413#410—21no—
414#410C22×C5911yescharacteristic
415#410C22×C5911yescharacteristic
416#354C22×C5912yescomplemented
417#353C22×C5912yescomplemented
418#352C22×C5914yescomplemented
419AΣL(1,𝔽16)C22×C5914yescomplemented
420C59#3356011yescharacteristic, direct product factor, Sylow
4212−1+4—21no—
4222−1+4—41no—
423H(5,𝔽2)—21no—
424H(5,𝔽2)—21no—
425H(5,𝔽2)—41no—
426H(5,𝔽2)C23×C5912yes—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—42no—
432C2×#41D4×C5911yescharacteristic, complemented
433C2×#41C23×C5911yescharacteristic
434C22×Q8D4×C5911yescharacteristic, complemented
435C22×D4D4×C5911yescharacteristic
436#137—22no—
437#137—41no—
438AGL(1,ℤ/8)—22no—
439AGL(1,ℤ/8)—41no—
440#135—42no—
441C2×M16—21no—
442C4⋊Q8—21no—
443C4⋊Q8—41no—
444C4⋊Q8D4×C5911yescharacteristic, complemented
445#127—21no—
446#127—41no—
447#127C23×C5911yescharacteristic
448#126—22no—
449#126—22no—
450#126—22no—
451#125—21no—
452#125—22no—
453#124—21no—
454#124—22no—
455#124—21no—
456#124—21no—
457#124—41no—
458#124—41no—
459#124D4×C5911yescharacteristic, complemented
460#124C23×C5911yescharacteristic
461#123—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—24no—
466#123D4×C5912yescomplemented
467#123C23×C5912yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—42no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—22no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—42no—
486#120—22no—
487#120—24no—
488#120D4×C5912yes—
489#120C23×C5912yes—
490C4×Q8—21no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—22no—
497#117—22no—
498#117—22no—
499#117—21no—
500#117—21no—
501#117D4×C5911yescharacteristic
502#117D4×C5911yescharacteristic, complemented
503C2×C4⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C42D4×C5911yescharacteristic, complemented
506#104—22no—
507#104—22no—
508#101—21no—
509#100C23×C5912yes—
510#99—21no—
511#99—21no—
512#99—24no—
513#99—24no—
514#99C23×C5912yes—
515#99C23×C5912yes—
516C24C2×D4×C5912yes—
517#41—22no—
518#41—22no—
519#41—41no—
520#41—41no—
521#41—42no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—42no—
528#41—42no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—81no—
536#41—81no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—42no—
545C2×Q8C2×D4×C5911yescharacteristic
546C2×Q8C2×D4×C5911yescharacteristic
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—41no—
567C2×D4—44no—
568C2×D4C2×D4×C5911yescharacteristic
569C2×D4C2×D4×C5911yescharacteristic
570C2×D4C2×D4×C5911yescharacteristic
571C2×D4C24×C5911yescharacteristic
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—41no—
580C22×C4C2×D4×C5911yescharacteristic
581C22×C4C2×D4×C5911yescharacteristic
582C22×C4C2×D4×C5911yescharacteristic
583C22×C4C2×D4×C5912yes—
584Q16—42no—
585SD16—42no—
586SD16—42no—
587D8—42no—
588M16—22no—
589M16—41no—
590C2×C8—41no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—22no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—44no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4C2×D4×C5912yes—
623C22⋊C4C2×D4×C5912yes—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—41no—
629C42—41no—
630C42C2×D4×C5911yescharacteristic
631C42C2×D4×C5911yescharacteristic
632C23—22no—
633C23—22no—
634C23—22no—
635C23—21no—
636C23—41no—
637C23—42no—
638C23—82no—
639C23#120×C5911yescharacteristic
640C23C22×D4×C5911yescharacteristic
641C23C22×D4×C5911yescharacteristic
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—81no—
651D4—22no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667D4—82no—
668D4—82no—
669D4—82no—
670D4—81no—
671D4—81no—
672D4—82no—
673D4—164no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—81no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4#120×C5911yescharacteristic
703C2×C4#120×C5911yescharacteristic
704C2×C4#120×C5911yescharacteristic
705C2×C4C22×D4×C5911yescharacteristic
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—82no—
721C22—84no—
722C22—82no—
723C22—161no—
724C22C2×#120×C5911yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—82no—
736C4—82no—
737C4C59×B(4,𝔽2)11yescharacteristic
738C4C59×B(4,𝔽2)11yescharacteristic
739C2—21no—
740C2—41no—
741C2—41no—
742C2—41no—
743C2—82no—
744C2—81no—
745C2—82no—
746C2C2×C59×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C59C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C59
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C59 ◁ C2×C4×C59 ◁ C2×#41×C59 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C59×#3551C2semidirect
2. C59×#3028C2semidirect
3. C59×#3027C2semidirect
4. C59×#3018C2semidirect
5. C59×#2200C2semidirect
6. C59×#2197C2semidirect
7. C59×#2126C2semidirect
8. C59×#2123C2semidirect
9. C59×#2122C2semidirect
13. C59×#560C22semidirect
17. C59×#551C22semidirect
43. C59×#354C22semidirect
44. C59×#353C22semidirect
45. C59×#352C22semidirect
46. C59×AΣL(1,𝔽16)C22semidirect
58. C2×#41×C59D4semidirect
60. C22×Q8×C59D4semidirect
70. C4⋊Q8×C59D4semidirect
85. #124×C59D4semidirect
92. #123×C59D4semidirect
128. #117×C59D4semidirect
131. C2×C42×C59D4semidirect
333. #33560C59direct (N × H)
366. #3551C2×C59semidirect
367. #3028C2×C59semidirect
368. #3027C2×C59semidirect
369. #3018C2×C59semidirect
370. #2200C2×C59semidirect
371. #2197C2×C59semidirect
372. #2126C2×C59semidirect
373. #2123C2×C59semidirect
374. #2122C2×C59semidirect
386. #560C22×C59semidirect
390. #551C22×C59semidirect
416. #354C22×C59semidirect
417. #353C22×C59semidirect
418. #352C22×C59semidirect
419. AΣL(1,𝔽16)C22×C59semidirect
420. C59#33560direct (N × H)
432. C2×#41D4×C59semidirect
434. C22×Q8D4×C59semidirect
444. C4⋊Q8D4×C59semidirect
459. #124D4×C59semidirect
466. #123D4×C59semidirect
502. #117D4×C59semidirect
505. C2×C42D4×C59semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C59×#35512
C59×#30282
C59×#30272
C59×#30182
C59×#22002
C59×#21972
C59×#21262
C59×#21232
C59×#21222
#3356059